Almost Periodic and Asymptotically Almost Periodic Solutions of Liénard Equations

The aim of this paper is to study the almost periodic and asymptotically almost periodic solutions on (0,+1) of the Li´enard equation x′′ + f(x)x′ + g(x) = F(t), where F : T ! R (T = R+ or R) is an almost periodic or asymptotically almost periodic function and g : (a, b) ! R is a strictly decreasing function. We study also this problem for the vectorial Li´enard equation. We analyze this problem in the framework of general non-autonomous dynamical systems (cocycles). We apply the general results obtained in our early papers [3, 7] to prove the existence of almost periodic (almost automorphic, recurrent, pseudo recurrent) and asymptotically almost periodic (asymptotically almost automorphic, asymptotically recurrent, asymptotically pseudo recurrent) solutions of Li´enard equations (both scalar and vectorial)

Folding of a donor–acceptor polyrotaxane by using noncovalent bonding interactions

Mechanically interlocked compounds, such as bistable catenanes and bistable rotaxanes, have been used to bring about actuation in nanoelectromechanical systems (NEMS) and molecular electronic devices (MEDs). The elaboration of the structural features of such rotaxanes into macromolecular materials might allow the utilization of molecular motion to impact their bulk properties. We report here the synthesis and characterization of polymers that contain π electron-donating 1,5-dioxynaphthalene (DNP) units encircled by cyclobis(paraquat-p-phenylene) (CBPQT4+), a π electron-accepting tetracationic cyclophane, synthesized by using the copper(I)-catalyzed azide-alkyne cycloaddition (CuAAC). The polyrotaxanes adopt a well defined “folded” secondary structure by virtue of the judicious design of two DNP-containing monomers with different binding affinities for CBPQT4+. This efficient approach to the preparation of polyrotaxanes, taken alongside the initial investigations of their chemical properties, sets the stage for the preparation of a previously undescribed class of macromolecular architectures

Charge generation in organic solar cell materials studied by terahertz spectroscopy

We have investigated the photophysics in neat films of conjugated polymer PBDTTPD and its blend with PCBM using terahertz time-domain spectroscopy. This material has very high efficiency when used in organic solar cells. We were able to identify a THz signature for bound excitons in neat PBDTTPD films, pointing to important delocalization in those excitons. Then, we investigated the nature and local mobility (orders of magnitude higher than bulk mobility) of charges in the PBDTTPPD:PCBM blend as a function of excitation wavelength, fluence and pump-probe time delay. At low pump fluence (no bimolecular recombination phenomena), we were able to observe prompt and delayed charge generation components, the latter originating from excitons created in neat polymer domains which, thanks to delocalization, could reach the PCBM interface and dissociate to charges on a time scale of 1 ps. The nature of the photogenerated charges did not change between 0.5 ps and 800 ps after photo-excitation, which indicated that the excitons split directly into relatively free charges on an ultrafast time scale

Excitonic Funneling in Extended Dendrimers with Non-Linear and Random Potentials

The mean first passage time (MFPT) for photoexcitations diffusion in a funneling potential of artificial tree-like light-harvesting antennae (phenylacetylene dendrimers with generation-dependent segment lengths) is computed. Effects of the non-linearity of the realistic funneling potential and slow random solvent fluctuations considerably slow down the center-bound diffusion beyond a temperature-dependent optimal size. Diffusion on a disordered Cayley tree with a linear potential is investigated analytically. At low temperatures we predict a phase in which the MFPT is dominated by a few paths.Comment: 4 pages, 4 figures, To be published in Phys. Rev. Let

Disorder and Funneling Effects on Exciton Migration in Tree-Like Dendrimers

The center-bound excitonic diffusion on dendrimers subjected to several types of non-homogeneous funneling potentials, is considered. We first study the mean-first passage time (MFPT) for diffusion in a linear potential with different types of correlated and uncorrelated random perturbations. Increasing the funneling force, there is a transition from a phase in which the MFPT grows exponentially with the number of generations $g$, to one in which it does so linearly. Overall the disorder slows down the diffusion, but the effect is much more pronounced in the exponential compared to the linear phase. When the disorder gives rise to uncorrelated random forces there is, in addition, a transition as the temperature $T$ is lowered. This is a transition from a high-$T$ regime in which all paths contribute to the MFPT to a low-$T$ regime in which only a few of them do. We further explore the funneling within a realistic non-linear potential for extended dendrimers in which the dependence of the lowest excitonic energy level on the segment length was derived using the Time-Dependent Hatree-Fock approximation. Under this potential the MFPT grows initially linearly with $g$ but crosses-over, beyond a molecular-specific and $T$-dependent optimal size, to an exponential increase. Finally we consider geometrical disorder in the form of a small concentration of long connections as in the {\it small world} model. Beyond a critical concentration of connections the MFPT decreases significantly and it changes to a power-law or to a logarithmic scaling with $g$, depending on the strength of the funneling force.Comment: 13 pages, 9 figure

Dynamics & Predictions in the Co-Event Interpretation

Sorkin has introduced a new, observer independent, interpretation of quantum mechanics that can give a successful realist account of the 'quantum microworld' as well as explaining how classicality emerges at the level of observable events for a range of systems including single time 'Copenhagen measurements'. This 'co-event interpretation' presents us with a new ontology, in which a single 'co-event' is real. A new ontology necessitates a review of the dynamical & predictive mechanism of a theory, and in this paper we begin the process by exploring means of expressing the dynamical and predictive content of histories theories in terms of co-events.Comment: 35 pages. Revised after refereein

Resist materials for 157-nm microlithography: an update

Fluorocarbon polymers and siloxane-based polymers have been identified as promising resist candidates for 157 nm material design because of their relatively high transparency at this wavelength. This paper reports our recent progress toward developing 157 nm resist materials based on the first of these two polymer systems. In addition to the 2-hydroxyhexafluoropropyl group, (alpha) -trifluoromethyl carboxylic acids have been identified as surprisingly transparent acidic functional groups. Polymers based on these groups have been prepared and preliminary imaging studies at 157 nm are described. 2-Trifluoromethyl-bicyclo[2,2,1] heptane-2-carboxylic acid methyl ester derived from methyl 2-(trifluoromethyl)acrylate was also prepared and gas-phase VUV measurements showed substantially improved transparency over norbornane. This appears to be a general characteristic of norbornane-bearing geminal electron-withdrawing substituents on the 2 carbon bridge. Unfortunately, neither the NiII nor PdII catalysts polymerize these transparent norbornene monomers by vinyl addition. However, several new approaches to incorporating these transparent monomers into functional polymers have been investigated. The first involved the synthesis of tricyclononene (TCN) monomers that move the bulky electron withdrawing groups further away from the site of addition. The hydrogenated geminally substituted TCN monomer still has far better transparency at 157 nm than norbornane. The second approach involved copolymerizing the norbornene monomers with carbon monoxide. The third approach involved free-radical polymerization of norbornene monomers with tetrafluoroethylene and/or other electron-deficient comonomers. All these approaches provided new materials with encouraging absorbance at 157 nm. The lithographic performance of some of these polymers is discussed

Light to Shape the Future: From Photolithography to 4D Printing

Over the last few decades, the demand of polymeric structures with well-defined features of different size, dimension, and functionality has increased from various application areas, including microelectronics, biotechnology, tissue engineering, and photonics, among others. The ability of light to control over space and time physicochemical processes is a unique tool for the structuring of polymeric materials, opening new avenues for technological progress in different fields of application. This article gives an overview of various photochemical reactions in polymers, photosensitive materials, and structuring techniques making use of light, and highlights most recent advances, emerging opportunities, and relevant applications

Single-molecule experiments in biological physics: methods and applications

I review single-molecule experiments (SME) in biological physics. Recent technological developments have provided the tools to design and build scientific instruments of high enough sensitivity and precision to manipulate and visualize individual molecules and measure microscopic forces. Using SME it is possible to: manipulate molecules one at a time and measure distributions describing molecular properties; characterize the kinetics of biomolecular reactions and; detect molecular intermediates. SME provide the additional information about thermodynamics and kinetics of biomolecular processes. This complements information obtained in traditional bulk assays. In SME it is also possible to measure small energies and detect large Brownian deviations in biomolecular reactions, thereby offering new methods and systems to scrutinize the basic foundations of statistical mechanics. This review is written at a very introductory level emphasizing the importance of SME to scientists interested in knowing the common playground of ideas and the interdisciplinary topics accessible by these techniques. The review discusses SME from an experimental perspective, first exposing the most common experimental methodologies and later presenting various molecular systems where such techniques have been applied. I briefly discuss experimental techniques such as atomic-force microscopy (AFM), laser optical tweezers (LOT), magnetic tweezers (MT), biomembrane force probe (BFP) and single-molecule fluorescence (SMF). I then present several applications of SME to the study of nucleic acids (DNA, RNA and DNA condensation), proteins (protein-protein interactions, protein folding and molecular motors). Finally, I discuss applications of SME to the study of the nonequilibrium thermodynamics of small systems and the experimental verification of fluctuation theorems. I conclude with a discussion of open questions and future perspectives.Comment: Latex, 60 pages, 12 figures, Topical Review for J. Phys. C (Cond. Matt